Biochemical Engineering Journal Oxygen transfer and mixing in mechanically agitated - PDF document

Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Nomenclaturegas–liquidinterfacialareaperunitdispersionvolume(mgas–liquidinterfacialareaperunitliquidvolume(mcross-sectionalareaofdowncomer(mcross-sectionalareaofriser(minstantaneousconcentrationofdissolvedoxygen(kmolmconcentrationofsuspendedsolids(kgminitialconcentrationofdissolvedoxygen(kmolmsaturationconcentrationofdissolvedoxygen(kmolmmeanbubblediameter(m)columndiameter(m)spargerholediameter(m)diameteroftheimpeller(m)diameterofdraft-tube(m)tankdiameter(m)diffusivityofthetransferringgasinliquid(mfractionalapproachtoequilibriumdenedbyEq.(5)masstransferefciencydenedbyEq.(22)Flimpellerownumbergravitationalacceleration(msverticaldistancebetweenpHelectrodes(m)gas–liquidmasstransfercoefcient(msoverallvolumetricgas–liquidmasstransfercoefcient(sconsistencyindex(Pasowbehaviorindexrotationalspeedoftheimpeller(stotalpowerinput(W)powerinputduetogassing(W)powerinputduetoagitator(W)Poimpellerpowernumbervolumeowrateofgas(mvolumeowrateofliquid(mreynoldsnumberoftheimpellertime(s)timeintervalbetweentracerresponsepeaks(s)initialorstarttime(s)supercialgasvelocitybasedonthetotaldowncomercross-section(mssupercialgasvelocityintheriserzone(msvolumeofliquid(mlinearliquidvelocityinthedowncomer(msexponentinEq.(13)concentrationofsuspendedsolids(%w/v)exponentinEq.(13) GreeklettersParameterinEq.(13)Averageshearrate(sOverallfractionalgasholdupGasholdupinthedraft-tubeApparentviscosityoftheuid(Pas)Viscosityofliquid(Pas)Densityoftheliquid(kgmInterfacialtension(Nm Fig.1.Thehydrofoilimpeller-agitatedairliftbioreactor.havebeenevaluatedforuseinbioreactorsinthepast,butmostlyonlyintheconventionalbafedstirredtankcong-uration[16–20].Afewstudieshavebeenreportedinreac-torswithaxialowmarinepropellersinsidedraft-tubes,butonlyinrelativelysmall(250l)vessels[6,11,21,22].2.Materialsandmethods2.1.ThereactorsanduidsMeasurementsweremadeinaconcentricdraft-tubebiore-actor(Fig.1)thatwasagitatedwithtwoidenticaldownward Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Fig.2.TheProchemMaxoTimpeller.pumpingProchemMaxoThydrofoilimpellers(Fig.2).The5-bladedimpellers,0.32mindiameter,weremountedona0.039mdiametershaftplacedatthecenterlineofthebioreactorvessel.Theverticaldistancebetweentheim-pellerswas0.68mandthelowerimpellerwaslocated1.02mfromthebottomofthetank.Thebioreactorvesselwas0.755mindiameteranditsoverallheightwas3.21m.Thedraft-tube,0.50mininter-naldiameterand2.06mtall,waslocated0.21mabovethebottomofthetank.Thevesselwasspargedintheannu-larzonethroughaperforatedpiperingsparger(96holesof0.002mindiameterlocatedontwoconcentricspargerringsof0.013mtubediameter).Theratiowas1.27.Theworkingvolumeandtheoverallvolumeofthebioreac-torwere1.10and1.46m,respectively.Thebioreactorwasmadeofstainlesssteel;twoverticalglasswindowsonthesidewallsofthevesselallowedinspectionoftheliquidlevel.Thestaticliquidheightwas2.46minallexperiments.Theimpellerswereagitatedwitha3hpmotor(575V,3-phase,3.9A)andavariablespeedgearbox.Adissolvedoxygenelectrode(YSI5739dissolvedoxy-genandtemperatureprobewithstandardmembrane;YellowSpringsInstruments,YellowSprings,OH,USA)andtwopHprobeswerelocatedinthedowncomer(Fig.1).Theoxygenelectrodewaspositionedataradialdistanceof0.24mfromthecenterlineofthevesseland2.15mabovethebottomofthetank.TheverticaldistancebetweenthetwoidenticalpHprobeswas1.39m;thelowerprobewas0.69mabovethebaseofthetankanddirectlybelowtheupperpHprobe.Theprobeswereplacedat0.15mradialdistancefromthecenterlineofthevessel.Thereactorwasspargedwithairornitrogen.Theuidsusedwerehardtapwater,aqueoussodiumchloride(0.15M)solutionintapwater,and2–4%(w/v,g/100ml)suspensionsofSolkaFloc(SF)cellulosebersinaqueoussodiumchlo-ride(0.15M).Theslurriesusedwerepreviouslyshowntosimulatewellthepulplikemycelialgrowthoftypicalfun-galfermentations[1].SF(gradeKS1016;FiberSales&Development,Urbana,USA)bershadanaveragelengthofmandabulkdensityof175kgm.TheTylerstan-dardscreenanalysiswasasfollows:1.4%on35mesh,2.0%on48mesh,5.2%on65mesh,12.6%on100mesh,78.8%through100mesh,39.0%on200meshand39.8%through200mesh.TheSFslurriesbehavedasnon-Newtonianpowerlawuidsandtheirconsistency()andow()indicescouldbeestimatedwiththefollowingcorrelations:istheconcentrationofSFsolidsinkgm.Eqs.(1)and(2)arebasedonpreviouslyreportedproperties[1,23];thecorrelationcoefcientsfortheseequationswere0.996and0.998,respectively.ThedatausedinobtainingEqs.(1)and(2)hadbeenmeasuredat20Covertheap-proximateshearraterangeof1–80s[1].Thedensityoftheuidsrangedfrom998to1020kgmat20Thesurfacetensionofalluidswas75,aspreviouslyreported[1,23].TheSFcelluloseberslurriesinsaltsolutionsareknowntosimulatewelltherheologicalpropertiesofthebrothsofmycelialfungiandlamentousbacteria[1,23]growinginthenon-pelletedpulplikemorphology.ThecellulosebersresemblemyceliaandlamentsofPenicilliaAspergilliNeurosporaandstreptomyces.2.2.ThemeasurementsExperimentswereconductedbatchwisewithrespecttotheliquidortheslurryphase.Allmeasurementswereat22C.Airfrom20MPamainswassuppliedtothereactorthroughalter,pressureregulator,owcontrolvalveandrotameter.Theowarrangementwassuchthattheaircouldbesubstitutedinstantaneouslywithnitrogenfromcylinders.Gasholdup,orthevolumefractionofgasindispersion,wasmeasuredbythevolumeexpansionmethod[1].Thein-terstitialliquidvelocitywasmeasuredinthedraft-tubebytheacidtracertechnique[1].Priortothemeasurements,theliq-uidwasfreedofcarbonate/bicarbonatebufferingbylower-ingthepHto4andbubblingwithair(085ms45min)whileagitating(200rpm).Afterthistreatment,theliquidshowednobufferingoverthepHrangethemeasurements.Formeasuringthetracerresponse,con-centratedsulfuricacid(6M,30ml)waspouredinstanta-neouslyontheliquidsurfaceabovetheriserzone,0.28mradialdistancefromthecenterlineofthevessel.ThepHresponsewasfollowedattwodownstreamlocationsinthedraft-tube.Theliquidvelocity()wascalculatedfromthemeasuredtimeinterval()betweenthetracerresponsepeaksfromthetwopHelectrodesandtheknowndistancebetweenthem;thus ConcentratedsodiumhydroxidewasusedtoreturnthepH4aftereachmeasurement.Amaximumof28mea-surementsweretakenduringadayandthisincreasedthesalt(sodiumsulfate)concentrationintheuidbylessthan0.006M,whichdidnotaffectthehydrodynamicproper-tiesofthehardtapwaterandtheslurries.Themixingtimewasdeterminedwiththeacidtracermethod[1], Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153asthetimeneededforthetracerconcentrationtoreach95%ofitsnalsteady-statevaluefromtheinstanceoftracerinput.Theoverallgas–liquidvolumetricmasstransfercoef-wasmeasuredwiththewell-knowndynamicgassing-inmethod[1,24,25].Twoindependentmeasure-mentsweremadesimultaneouslyusingtwodissolvedoxy-genelectrodes,locatedasnotedinFig.1.Insomecases,additionalmeasurementsweremadewiththetwo-probeassembly(Fig.1)movedtotheradialmidpointoftheriserzoneandwithoutchangingtheheightsofthetwooxygenelectrodes.Forthemeasurements,theuidwasdeaeratedbybubblingwithnitrogenuntilthedissolvedoxygencon-centrationhaddeclinedtobelow5%ofairsaturation.Thenitrogenowwasthenstopped,thebubbleswereallowedtodisengage,apresetowofairwasnowestablished,andtheincreaseindissolvedoxygenconcentrationwasfollowedwithtimeuntiltheuidbecamenearlysaturatedwithoxygen.Thewascalculatedastheslopeofthelinearequation,thefractionalapproachtoequilibrium[1],isgiven InEq.(5),isthesaturationconcentrationofdissolvedtheinitialconcentrationofdissolvedoxygenatwhenahydrodynamicsteady-statehasbeenreestab-lished(1min)uponcommencementofaerationanddissolvedoxygenconcentrationatanytime[1,25].Theisessentiallytheratiooftheinstantaneousmasstransferratetothemaximumpossiblerateofoxygentransfer[1].Thespecicpowerinputduetoaerationwascalculated[1,14]usingtheequation L LgUGr isthepowerinputduetoaeration,thecul-turevolume,thegravitationalacceleration,thecross-sectionalareaofthedowncomerzoneandcross-sectionalareaoftheriserzone.Thesupercialgasve-locity()inEq.(6)isbasedonthecross-sectionalareaoftheriserzone.ThepowerinputduetomechanicalagitationwasestimatedusingthepowernumberversustheimpellerReynoldsnumbercurvesfortheProchemimpeller[17].Forestimatingthemechanicalpower,theimpellerReynoldsnumber()wasdenedasfollows: istheimpellerdiameter,therotationalspeedoftheimpellerandtheapparentviscosityoftheuid.TheapparentviscosityinEq.(7)wasestimatedwiththepowerlawequationwheretheaverageshearratedependedontherotationalspeedoftheimpeller[26,27],asfollows:-and-valuesfortheslurrieswereobtainedwithEqs.(1)and(2),respectively.Themechanicalpowerinput()relatedwiththepowernumberfromthepowercurves[2,17],asfollows:wherePoisthepowernumber.Thetotalwastwicethevaluecalculatedforoneimpeller[27].TheimpellerpowerdrawwasnotcorrectedforthepresenceofgasbecauseforProchemhydrofoilstheaerationoftheuidisknowntohaveonlyamarginalimpact(5%)onthepowercurverelativetothatintheunaerateduid[17]whentheairownumberissmall.Also,thedowncomerzonewheretheimpellerswerelocatedwasnotdirectlyspargedwiththegas.Thetotalspecicpowerinputintheuidwasobtainedasfollows: LGM InEq.(11),isthetotalpowerinput,thevolumeofthepowerinputduetoaerationandthepowerinputduetomechanicalmixing.3.Resultsanddiscussion3.1.GasholdupThefractionalgasholdupincreasedwithincreasingaera-tionandagitationrates,asshowninFig.3,whichwastyp-icalforalltheuidsused.Inallcases,theholdupinitially Fig.3.Effectofimpelleragitationspeedandtheaerationvelocityontheoverallgasholdupin2%SFslurry. Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Fig.4.Effectoftheimpelleragitationspeed,theaerationvelocityandthesolidsconcentrationongasholdup.roserapidlywithincreasinggasvelocityuntilanincreasingrateofbubblecoalescencereducedtherateofriseinholdup(Fig.3).Bubblyowregimeinwhichthebubblesrosewithrelativelyfewinteractionsamongthem,persisteduntilagasvelocityof0.05ms.Athigheraerationrate,thecoa-lescedbubbleow(churnturbulentow)occurredandarapidriseinholdupwasagainobserved(Fig.3)becauseoftheformationoflargesphericalcapbubbles.Inmechani-callyagitateduids,somegasholduppersistedbecauseofsurfaceentrainmentevenintheabsenceofspargedaeration.Atagivenaerationvelocityandagitationrate,theholdupdeclinedwithincreasingconcentrationofthecellulosebersolidsintheslurry(Fig.4).Themaximumreductioninholdupwas60%relativetothevalueinthesolids-freesys-tem.Theholdupreducingeffectofsolidswasassociatedwiththeirturbulencedampeningeffect.Theaverageerroringasholdupmeasurementswaslessthan3%.3.2.Gas–liquidmasstransferInthedynamicmeasurementof,theassumptionregardingthestateofmixednessinthereactorcaninuencethecalculatedvalueofthe.Awell-mixedliquidphasewasassumedtoexistinthiswork,inkeepingwithpriorknowledgeofsimilarsystems[1].Despitealargevolumeofuid(1.1m),theassumedwell-mixedstatewasapproachedclosely,asconrmedinFig.5where,forgivenagitationandaerationrates(i.e.thedatawithinacluster)thevaluesobtainedwiththedissolvedoxygenprobeslocatedinwidelyspacedregionsofthereactor(eitherinriserorindowncomer)showedgoodmutualagreement,generallywithin6%ofthemeanvalueforthetwolocations.ThedatainFig.5arefortheair–watersystemunderextremestatesofaerationandmechanicalagitation.Mixingwasnoticeablypooreratallgasowratesintheairliftmodeofoperation0rpm)comparedtowhentheagitatorwasused.ThisisreectedinFig.5wherethedifferencebetweenthe Fig.5.Effectofthepositioningofthedissolvedoxygenelectrodeontheforvariousintensitiesofaerationandmechanicalagitation.topandthebottomvaluesmeasuredinthedowncomerisgenerallygreaterintheabsenceofmechanicalmixing.Becausethelocationoftheprobeshadarelativelyminoreffectonthecalculated,thesubsequentmeasurementswereperformedonlyattheupperlocationinthedown-comer.Theuidmixingtime(seeSection3.3)of30–55swasalwayslessthan1/.Similarly,theresponsetimeofthedissolvedoxygenelectrodes(10sfor63%offullscaleresponse)wasalwaysand,therefore,theelectroderesponsedelayscouldbeneglectedincalculationofthe[1,28].TheaverageerrorinthewasThetypicaldependenceoftheonthetwomainoperationalvariables(i.e.agitationspeed,aerationrate)isshowninFig.6forthe2%slurryofSF.Thebehaviorshown(Fig.6)isgenerallyconsistentwiththatobservedforgasholdup(Fig.3)becauseholdupisthemainfactorthatin-uencesthegas–liquidinterfacialarea.Thevaluewasenhancedbyincreasingaerationandagitationrates(Fig.6).Increasingconcentrationofsuspendedcellulosebersre-bothintheairlift0rpmandtheintensely200rpmhybridmodesofoperationofthereactor(Fig.7).Similarbehaviorhasbeenobservedinmanybrothsofmycelialfungi[1,5].Inviewofthewell-knowntheoreticalconsiderations[1,23],aplotofagainstthegasholdupratioisexpectedtobelinearinanyspargedbioreactor,irrespec-tiveoftheuidusedandtheprevailingowregime[1].Thishasbeendemonstratedinthepastforbubblecolumnsandairliftbioreactors[1,29].Inthemechanicallyagitatedhybridreactor,too,alineardependencebetweentheholdupratiowasobservedforthefullrangeoftheaerationratesandtheimpellerspeedstested(Fig.8).Thisbehaviorwasseeninalltheuidsexamined.Asexpected,theratio(:meanbubblediameter)calculatedfromthemeasuredvaluesofandthegasholdupaccordingtoapublishedprocedure[1,23],wascon- Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Fig.6.Effectofagitationspeedandaerationrateonin2%SFslurry. Fig.7.Effectofthesolidsconcentrationonin(a)theairliftand(b)thehybridmodesofoperationofthereactor.stantirrespectiveoftheagitationspeedandtheaerationrateused(Fig.9).ThepatterninFig.9wasrepresentativeofalltheuidstested,althoughthespecicvalueoftheratiodependedontheconcentrationofthecellulosebersintheslurry.Themeanexperimentalvalueofthetioin2%SFslurrywas0.0261s,orwithin47%ofthevaluecalculatedwiththeindependentlydevelopedempiri-cal[1,14,23]relationship B563105
gDL 2L L istheconcentrationofsuspendedsolidsin%w/v,thediffusivityofoxygeninthesuspendinguid,interfacialtension,theviscosityoftheliquidphaseandthedensityofthesuspendingliquid.NotethatEq.(12)wasdeveloped[1,14,23]inbubblecolumnsandairliftreactorsofentirelydifferentgeometriesthanthehybridcongurationofthepresentstudy.Thepublishedcorrelationsforinmechanicallyagitatedconventionaltanksareusuallyoftheform areconstantsforagivencombinationoftheuidandthegeometryofthebioreactor[25,28].Anexampleisthefollowingequation[30]fortheair–watersystem: 4TM L05510551 isthetankdiameterandtheproductofthecross-sectionalareaofthereactor.Asimilarcorrelatingapproachwasusedhere.dataforwaterinthebubbleowregime05mscorrelatedwiththeequation Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Fig.8.Themasstransfercoefcientfor2%SFslurriesundervariousconditionsofagitation.Thelineshownhasaunitslope. forboththeairliftandtheagitated-airliftmodesofopera-tion(Fig.10).ThepredictionsofEq.(15)agreedwiththemeasureddatawithin9.6%averagedeviation,orwithin15%maximumdeviation(Fig.10).Thedataforwaterinthechurnturbulentorthecoalescedbubbleowregime05mscorrelatedwiththeequation forboththeairliftandtheagitated-airliftmodesofopera-tion(Fig.11).ThepredictionsofEq.(16)agreedwiththe Fig.9.Effectofaerationvelocityandagitationspeedonthein2%slurryofSF.Thehorizontallineistheaverageofalldata.measureddatawithin5.6%averagedeviation,orwithin15%maximumdeviation.IndevelopingEqs.(15)and(16),dataforairliftmodesofoperation(noagitation)wererstcorrelatedintheform.Inthenextstage,thesupercialaerationvelocitywasvaried(forvariousxedvaluesofthemechanicalspecicpowerinput,)inthestirredair-liftmodeofoperation,toobtaindifferentmeasurementsof.Theresultingdatawereusedtogenerateasetof-values(onesetforeach),bylinearregres-sion.The-valueswereobservedtodependontheagitationand,therefore,best-tcorrelationsbetweenweregeneratedbyregression,forthetwoowregimes.The-valuewasseentodependon;hence,regressionwasusedtodeterminecorrelationsbetweenforthetwoowregimes.Acorrelationfortheoverallvolumetricgas–liquidmasstransfercoefcientintheannulusspargedconcentric-tube Fig.10.Predicted(Eq.(15))vs.measuredintheair–watersystem(bubbleow). Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Fig.11.Predicted(Eq.(16))vs.measuredintheair–watersystem(coalescedbubbleow).airliftvesselshasbeenreported[31],asfollows: !L225L L!L0500
L 3L L0136h wheretheoverallmasstransfercoefcient()dependsonfactorssuchasthegasholdup,thegravitationalac-,thesurfacetension,theviscosityoftheliquidphase,thedensityoftheliquidphase,thediffu-sivityofoxygenintheliquid,thediameterofthereactorcolumnandthediameterofthespargerholes.Eq.(17)wasdevelopedforthefollowingrangeofvari-ables:3"aspectratio6–15and23.TheaverageerrorinestimatingthewithEq.(17)was12%for175measurements[31].AsshowninFig.12,Eqs.(15)and(16) Fig.12.AcomparisonofEqs.(15)–(17)forpredictionintheairliftmodeofoperation.developedhereagreedexceptionallywellwithEq.(17)ofKoideetal.[31]andthisvalidatesourdata.OfcoursetheearlierdevelopedEq.(17)doesnotapplytoslurriesandhybridairliftreactorsandsothecomparisoninFig.12isstrictlyforoperationsinthepurelyairliftmode(i.e.0rpm)withtheair–watersystem.NotethattheoverallmasstransfercoefcientinEq.(17)isgivenintermsofthevolumeofthegas–liquiddispersionandnotintermsoftheliquidvolume.ForthecomparisoninFig.12,thevaluescalculatedwithEq.(17)wereexpressedintermsoftheusingthefollowing[1]exact Themeasuredgasholdupdata(seeSection3.1)wereusedforthecorrection.Theonlyothercorrelationsreportedforinmechan-icallystirredairliftreactorsarethoseofBangetal.[21];fortheair–watersystem,theyobtainedtheequation: L081M IncomparisonwithEqs.(15)and(16)obtainedbyus,Eq.(19)producesextremelyhighvaluesof.Also,Eq.(19)isinconsistentwithEq.(17)ofKoideetal.[31].Thereasonsforthisdisparityareapparentlylinkedwithim-portantdifferencesbetweenthereactorusedbyusandthatusedbyBangetal.[21].Thelatterauthorsemployedanexceptionallysmallvessel(10l)thatwasspargedinthedraft-tube;theratiowasonly0.69comparedtoourvalueof1.27;andamarineimpellerpumpingupwardwasusedinthedraft-tubecomparedtoourdownwardpumpinghydrofoilimpellers.dataforallSFslurriesinthebubbleowregime05mscorrelatedwiththeequation expforboththeairliftandtheagitated-airliftoperations(Fig.13).Inthechurnturbulentregime05msthedatafortheslurriescorrelatedwiththeequation exp Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Fig.13.Predicted(Eq.(20))vs.measuredintheSFslurries(bubbleow).forbothmodesofoperation(Fig.14).ThepredictionsofEq.(21)agreedwiththemeasureddatawithin19%aver-agedeviation.Thediminishingeffectofthesolidsispredominantlybecauseofthereductioningasholdupcausedbythesolidsandthisreducesthegas–liquidinterfacialareaformasstransfer.Also,anincreasingconcentrationofthecellulosebersolidshasbeenshowntoreducethevalueforagivenaveragebubblediameter[1,14].Conventionalmechanicalagitationisknowntoenhancerelativetovaluesobtainedintheabsenceofagitation;however,theenhancementindoesnotcompensatefortheincreasedpowerdemandofmechanicalagitationandthemasstransferefciencyisreducedinpresenceofagitation[1].Thisalsooccursinlow-poweragitationwithhydrofoilimpellers;thus,asshowninFig.15fortheair–watersys-temandthe3%slurryofSF,themasstransferefciencyislowerwithmechanicalagitationthaninpurelyairlift0rpm.Theefciencyisdenedas  Fig.14.Predicted(Eq.(21))vs.measuredintheSFslurries(coa-lescedbubbleow). Fig.15.Oxygentransferefciencyvs.totalspecicpowerinputundervariousconditionsofagitation.Bymultiplyingthe-valuewiththesteady-statedrivingforceforoxygentransfer(i.e.),wecanobtaintheamountofoxygentransferredperunitofenergysupplied.3.2.1.SurfaceaerationInthepast,manystudiescharacterizedgas–liquidmasstransferinrelativelysmallbioreactors[22,30]inwhichabsorptionatthesurfacecontributedsignicantlytothetotalmasstransfer.Generally,noattemptsweremadetodistinguishbetweenthecontributionsofthesurfaceandthesubmergedaeration.Inthisstudy,theforsurfaceaer-ationwasmeasuredundervariousconditionsofagitationandwithoutthesubmergedaeration.Theforsurfaceaeration(air–water)correlated(Fig.16)withtheimpellerspeedasfollows:ThecorrelationcoefcientforEq.(23)wasgreaterthan0.999.ThedependenceshowninEq.(23)isbecauseofthecombinedeffectsofonturbulenceandtheuidrenewal Fig.16.Effectofimpelleragitationspeedonforsurfaceaerationinwater. Y.Chisti,U.J.Jauregui-Haza/BiochemicalEngineeringJournal10(2002)143–153 Fig.17.Effectoftheimpelleragitationspeedandtheaerationvelocityonmixingtimeinthe2%SFslurry.rateatthesurface.Atthelowestaerationrateused0156ms,thecontributionofsurfaceaerationtothetotaloxygentransfervariedfrom1.5to11.6%,dependingonthespeedoftheimpeller.Inthiscase,theratiooftheliquidsurfaceareatothetotalvolumewasonly0.41;po-tentially,thesurfacecancontributemoretothetotalmasstransferinshallowreactorssuchasthoseusedforanimalcellculture[25].3.3.MixingandliquidvelocityThetypicalvariationofthemixingtimewithaerationandagitationratesisshowninFig.17.Inallcases,themixingimprovedwithincreasingratesofaerationandmechanicalagitation(Fig.17);however,theinuenceofaerationrateonmixingtimewasmostpronouncedonlyunderconditionsoflittleornomechanicalagitation.Atsufcientlyhighaerationvelocities04ms,themixingtimesobtainedintheabsenceofmechanicalagitationwerecomparabletothoseobtainedwiththeagitator-assistedoperation.Mixingtimewasnotsensitivetotheconcentrationofsolidsoverthe0–4%concentrationrange.Theaverageerrorinthemixingtimemeasurementswas9.4%.Thelinearliquidvelocityinthedowncomerincreasedwiththeincreasingspeedoftheagitatorbutwasnotsensi-tivetotheaerationrate(Fig.18),exceptintheairliftmodeofoperation0rpm.Thefactthattheliquidvelocityvariedlittlewithaerationrateinmechanicallyagitatedoper-ation(Fig.18)whereasataconstantagitationspeedthemix-ingtimedeclinedwithincreasingrateofaeration(Fig.17)suggeststhatundergivenconditionsofmechanicalmixing,thegasbubblesrisingthroughtheuidwereanimportantcauseofmixing.Bubblingfrequencyincreaseswithincreas-ingaerationrateandthebubblesrisingrelativetotheliquidcarryintheirwakesacertainamountofuid.Asnotedear-lier,theeffectofmechanicalagitationonmixingtimewaspronouncedonlyatrelativelylowaerationrates(Fig.17).At Fig.18.Effectoftheimpelleragitationspeedandtheaerationvelocityontheaverageliquidvelocityinthedowncomer(air–water).higheraerationvelocities04ms,risingbub-blesseemedtothedominantcauseofthemixing(Fig.17).Intheair–watersystem,theowwasalwaysinthede-velopedturbulentregimewhenevertheagitatorwasused110rpmandtheimpellerReynoldsnumberexceeded.Inthisregime,theimpellerownumberisaconstantandavalueof0.82hasbeenreportedfortheownumberfortheProchemMaxoTimpeller[2].Becauseoftheconstantownumber,therateofpumping)bytheimpellershouldvarylinearlywiththeagitationspeed,asfollows:ThedatainFig.18suggestanon-linearrelationshipbetweentheimpellerspeedandtheaverageliquidvelocity(measuredinthedraft-tube.Becausetherelatedexactly[1]asfollows:thediscrepancybetweenEq.(24)andthebehaviorinFig.18isexplainedbyanon-lineardependencebetweenandthegasholdupinthedowncomer,.Theaverageerrorintheliquidvelocitymeasurementswas7.7%.Unlikewiththeair–watersystem,theowregimeformixingoftheSFslurrieswastransitionalbecauseofthehighapparentviscositiesoftheslurries.4.ConcludingremarksInviewoftheobservationsdiscussed,theprincipalcon-clusionsareasfollows:1.Useoflow-poweraxialowimpellersinthedowncomerofanairliftbioreactorcansubstantiallyenhancetherateofliquidcirculation,mixingandgas–liquidmasstrans-ferrelativetooperationwithouttheagitator;however, 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